The Global Positioning System (GPS) is a collection of 24 earth-orbiting satellites. Each of the GPS satellites travels in a precise orbit about 11,000 miles above the earth's surface. A GPS receiver locks onto at least 3 of the satellites, and responsive, thereto, is able to determine its precise location. Each satellite transmits a signal modulated with a unique pseudo-noise (PN) code. Each PN code comprises a sequence of 1023 chips which are repeated every millisecond consistent with a chip rate of 1.023 MHz. Each satellite transmits at the same frequency. For civil applications, the frequency is known as L1 and is 1575.42 MHz. The GPS receiver receives a signal which is a mixture of the transmissions of the satellites that are visible to the receiver. The receiver detects the transmission of a particular satellite by correlating the received signal with shifted versions of the PN code for that satellite. If the level of correlation is sufficiently high so that there is a peak in the level of correlation achieved for a particular shift and PN code, the receiver detects the transmission of the satellite corresponding to the particular PN code. The receiver then uses the shifted PN code to achieve synchronization with subsequent transmissions from the satellite.
The receiver determines its distance from the satellite by determining the code phase of the transmission from the satellite. The code phase (CP) is the delay, in terms of chips or fractions of chips, that a satellite transmission experiences as it travels the approximately 11,000 mile distance from the satellite to the receiver. The receiver determines the code phase for a particular satellite by correlating shifted versions of the satellite's PN code with the received signal after correction for Doppler shift. The code phase for the satellite is determined to be the shift which maximizes the degree of correlation with the received signal.
The receiver converts the code phase for a satellite to a time delay. It determines the distance to the satellite by multiplying the time delay by the velocity of the transmission from the satellite. The receiver also knows the precise orbits of each of the satellites. Updates to the locations of the satellites are transmitted to the receiver by each of the satellites. This is accomplished by modulating a low frequency (50 Hz) data signal onto the PN code transmission from the satellite. The data signal encodes the positional information for the satellite. The receiver uses this information to define a sphere around the satellite at which the receiver must be located, with the radius of the sphere equal to the distance the receiver has determined from the code phase. The receiver performs this process for at least three satellites. The receiver derives its precise location from the points of intersection between the at least three spheres it has defined.
The Doppler shift (DS) is a frequency shift in the satellite transmission caused by relative movement between the satellite and the receiver along the line-of-sight (LOS). It can be shown that the frequency shift is equal to νLOS/ν, where νLOS is the velocity of the relative movement between the satellite and receiver along the LOS, and λ is the wavelength of the transmission. The Doppler shift is positive if the receiver and satellite are moving towards one another along the LOS, and is negative if the receiver and satellite are moving away from one another along the LOS.
The Doppler shift alters the perceived code phase of a satellite transmission from its actual value. Hence, the GPS receiver must correct the satellite transmissions for Doppler shift before it attempts to determine the code phase for the satellite through correlation analysis.
The situation is illustrated in FIG. 1, which shows a GPS receiver 10 and three GPS satellites 12a, 12b, and 12c. Each satellite 12a, 12b, and 12c is transmitting to the OPS receiver 10. Satellite 12a is moving towards the GPS receiver 10 along the LOS at a velocity νa+14; satellite 12b is moving away from the GPS receiver 10 along the LOS at a velocity νb−16; and satellite 12c is moving away from the GPS receiver 10 along the LOS at a velocity νc−18. Consequently, assuming a carrier wavelength of λ, the transmission from satellite 12a will experience a positive Doppler shift of             v      a      +        λ    ;the transmission from satellite 12b will experience a negative Doppler shift of             v      b      -        λ    ;the transmission form satellite 12c will experience a negative Doppler shift of             v      c      -        λ    .
One system for correcting for the Doppler shift is described in commonly assigned U.S. patent application, Ser. No. 09/145,055, filed Sep. 1, 1998, and entitled “DOPPLER CORRECTED SPREAD SPECTRUM MATCHED FILTER,” now U.S. Pat. No. 6,044,105, the disclosure of which is hereby incorporated by reference in its entirety. In the foregoing system, a Doppler generator produces a complex phase shift value (having real and imaginary components) that it combined with an incoming complex data sample prior to correlation with a PN code in a matched filter correlator, so that Doppler error is minimized. Although meritorious to an extent, this system still suffers from some Doppler error. Thus, there is still a need for ways to further improve correlation analysis by better compensating for Doppler shift.